Pivot point problems when "adjust edit cage to modifier result" selected on amature modifier
That's how blender works, it could/should be reported as a bug.

The mesh is deformed to match the armature during edit mode but the manipulator widget doesn't get the same deformation. If you toggle the edit cage display on/off you should see that the widget stays in the undeformed location of the selected face.

The same thing is happening with snapping the cursor.

While the widget is drawn visually in the wrong location it still functions correctly, as do the keyboard shortcuts G,S,R.